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Jun
25
comment In a Black-Scholes world, why must volatility be strictly increasing in time-to-expiration?
The points you raise make a lot of intuitive sense. However all of them allude to some sort of "soft" arbitrage. I was hoping someone could create some sort of arbitrage portfolio of the sort typically quoted when talking about option pricing (eg. zero initial value with non-zero future value). Also regarding point: "But the option with the longer maturity contains the maturity of the shorter option, so it must be worth at least as much." I can see how that could apply to American options but Black implies European and the later expiring option cannot subsume the earlier expiring one?
Jun
24
asked In a Black-Scholes world, why must volatility be strictly increasing in time-to-expiration?
Jun
4
awarded  Scholar
Jun
4
accepted Standard Deviation as listed in Rebonato's Volatility and Correlation: Binomial Replication 2.3.4 Worked-Out Example
Jun
4
comment Standard Deviation as listed in Rebonato's Volatility and Correlation: Binomial Replication 2.3.4 Worked-Out Example
Excellent thank you!
Jun
4
comment Standard Deviation as listed in Rebonato's Volatility and Correlation: Binomial Replication 2.3.4 Worked-Out Example
I'm afraid this answer makes too many assumptions outside of the framework set up in the context of the Worked-Out Example in question. In the example, the pricing is approached from a "market price of risk" angle. I am trying to figure out how he came to the formula for standard deviation without all the implicit assumptions and framework of a tree.
Jun
3
awarded  Student
Jun
3
asked Standard Deviation as listed in Rebonato's Volatility and Correlation: Binomial Replication 2.3.4 Worked-Out Example